Rigid body refinement

Up to now we have seen how lattice distortions are detected and characterized. This does not provide a direct observation of the molecular translations, rotations, and deformations associated with the distortion. However, for a few compounds it has been possible to measure a large enough number of satellite or superstructure reflections so that the distorted structure can be parametrized and refined (rigid-body or full structural study). We consider below four examples, taken from materials selected in Section IV. A, which show that such studies are not easy and that the data collection requires special attention. Indeed, it is generally difficult to measure enough satellite reflections, especially if several kinds of the latter coexist (e.g., 2kp and 4kF satellites, high-order satellites, etc.). 

Jones, P.G. (1988) The distortion of pentafiuorophenyl groups in metal complexes limitations of rigid-body refinement. Journal of Organometallic Chemistry, 345(3), 405-411. 

The chitobiose unit has been treated as a rigid body, and by using the full-matrix, least-squares, rigid-body, refinement procedure, the structure was refined to an R factor of 40.7%. Visually estimated intensities were used. The structure was found to be free from short contacts, and to be stabilized by an intrachain OH-3—0-5 hydrogen-bond and one interchain N-H—O hydrogen-bond. 

Usually, the top peaks of the translation search are then submitted to a low resolution quick rigid-body refinement, for which quick algorithms have been devised (Huber and Schneider, 1985 Navaza and Saludjian, 1997).The resolution is usually taken to be 12-4 Angstroms or so if one wants to use the low resolution terms, one should use a solvent effect correction technique (Fokine and Urzhumtsev, 2002). 

Sometimes, it is not so easy to convince oneself that the solution of the molecular replacement problem has, in fact, been found, even after rigid-body refinement indeed, the first solution is not always well detached and different scores may produce different rankings. The most commonly used scores are correlation coefficients on either intensities or structure-factor amplitudes, and R-factors. Even though these criteria are formally related (Jamrog et ah, 2004), they can produce different rankings, especially if no solution is clearly detached. Some other criterion is then needed to discriminate between the potential solutions. 

The need for automated protocols is apparent from the strategy adopted by AMoRe to circumvent the problem that the score of the rotation function (RF) is far from being perfect and does not always rank the solutions correctly (Navaza, 2001). Indeed, it is often observed that the true solution is not the top solution, with many false positives. Hence, AMoRe runs a translation function (TF) for each of, typically, the top 50 or 100 solutions of the rotation function. This is actually quite rapid as TF is based on FFT then, the first 10 solutions of each of these TF runs is in turn refined using a very effective implementation of rigid-body refinement (Navaza, 2001). 

If there is NCS in the crystal, all molecules of the asymmetric unit must be searched in turn every time a potential solution has been found, it is possible to use this information to increase the signal-to-noise ratio of the searches for the other molecules. But then, the combinatorics of testing the 50 top solutions of the rotation function and then the 10 top solutions of each associated translation function for rigid-body refinement cannot be done by hand as in the previous case, as soon as there is more than two molecules in the asymmetric unit. In NCS-MR, depending on the number of molecules present in the asymmetric unit, there are thousands of possibilities to be searched. Also, as one is searching with only a fraction of the asymmetric unit, the signal to be expected is intrinsically lower. 

Corn Coeff. = 38%), but the best refined model was Model 23 with Rwork = 43.8% and Rfree = 52% this kind of score could never be obtained with only Rigid Body refinement. 

The initial model of ALBP was built by simply putting the amino acid sequence of ALBP into the molecular structure of myelin P2 protein. After a 20-step rigid-body refinement of the positions and orientations of the molecule, crystallographic refinement... 

Next, the side chains of P2 were replaced with the side chains of ALBP at corresponding positions in the amino-acid sequence to produce the first ALBP model. The position and orientation of this model were refined by least squares, treating the model as a rigid body. Subsequent refinement was by simulated annealing. At first, all temperature factors were constrained at 15.0 A2. After the first round of simulated annealing, temperature factors were allowed to refine for atoms in groups, one value of B for all backbone atoms within a residue and another for side-chain atoms in the residue. 

Each refined orientation of the probe received a correlation coefficient that shows how well it fits the Patterson map of ALBP. The orientation receiving the highest correlation coefficient was taken as the best orientation of the probe, and then used to refine the position of the probe in the ALBP unit cell. The orientation and position of the model obtained from the molecular replacement search was so good that refinement of the model as a rigid body produced only slight improvement in R. The authors attribute this to the effectiveness of the Patterson correlation refinement of model orientation, stage two of the search. 

What is apparent from the examples above is that, in most cases, the key problem is the measuring of a large enough number of weak (or even very weak) satellites or superstructure reflections. A limited data set forces the use of rigid-body refinements and may lead to inaccurate results. However, we may expect that new, very high flux synchrotron sources may help to solve this problem in the near future. 

The next refinement of the model takes into account that the shape of most molecular species differs from being rod-like typical nematogenic molecules are given in Table 4.6-1. The resulting behaviour of such a bi-axial molecule is often associated with hindered rotation, however it can also be understood from a rigid-body model where different moments of inertia lead to oscillations of different angular amplitudes in spite of identical (thermal) excitation and identical repulsive forces (Korte, 1983). This can be summarized by order parameters defined as above but referring to one of the two shorter. 

Solution of crystal structures can be aided by rigid body refinement of a molecular mechanics optimized structure. A recent example of this is the work of Boeyens and Oosthuizen. The crystal structures of (15-ane N5)Cu(II) and (16-ane N5)Ni(II) were refined with the aid of calculated models from a force field described earlier. This method, however, does not refine the internal molecular parameters. 

---